Get instance of Swiper from DOM

swiper.js

// This example shows us how to update broken swiper after Fancybox carousel closing
if (typeof fancyboxInit !== undefined) {
  // Main approach here is the next row  
  $.fancybox.defaults.backFocus = false;
  let showCaseSlider = $('.showCaseSlider .swiper-container');
  $('[data-fancybox]').fancybox({
    afterClose: function() {
      if (showCaseSlider) {
        let showCaseSliderInstance = showCaseSlider[0].swiper;
        showCaseSliderInstance.update();
      }
    }
  });
}

If you using typescipt. you can do:

import {Swiper} from "swiper/types"

interface SwiperInstance extends HTMLElement {
  swiper?: Swiper
}

...

const swiperElement = document.querySelector<SwiperInstance>(".your-swiper")
swiperElement.swiper?.update()

Thanks for the advice @ImKubass